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Permutations

Tool to generate permutations of items. In Mathematics, a permutation is an arrangement of distinct items in various orders 123,132,213,231,312,321.

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Permutations -

Tag(s) : Combinatorics

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Permutations

Permutations Generator

 Permutation of Digits/Numbers (from 1 to N) Letters (A,B,C...)
 Separator Comma ',' None

Permutations from List Generator

 Separator Comma ',' None

Random Permutation

⮞ Go to: Random Selection

What is a permutation? (Definition)

Item permutations consist in the list of all possible arrangements and ordering of elements in any order.

Example: The three letters A,B,C can be shuffled (anagrams) in 6 ways: A,B,C B,A,C C,A,B A,C,B B,C,A C,B,A

Permutations should not be confused with combinations (for which the order has no influence) or with arrangements also called partial permutations (k-permutations of some elements).

How to generate permutations?

The best-known method is the Heap algorithm (method used by this dCode's calculator).

Step 1 - for each item, fix it at the beginning

Step 2 - repeat step 1 with the remaining items

Permutations can thus be represented as a tree of permutations:

How to count permutations?

Counting permutations uses combinatorics and factorials

Example: For $n$ items, the number of permutations is equal to $n!$ (factorial of $n$)

How to count distinct permutations?

Having a repeated item involves a division of the number of permutations by the number of permutations of these repeated items.

Example: DCODE 5 letters have $5! = 120$ permutations but contain the letter D twice (these $2$ letters D have $2!$ permutations), so divide the total number of permutations $5!$ by $2!$: $5!/2!=60$ distinct permutations.

How to remove the limit when computing permutations?

Permutations make exponential values which need huge computing servers with huge memory cells, so the generation are not free.

Source code

dCode retains ownership of the online 'Permutations' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Permutations' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Permutations' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Permutations' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

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